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Re: Making a tree with "millions and millions" of dynamic nodes

From: Christian Fowler <google_at_NOSPAM.gravesweeper.com>
Date: Tue, 09 Dec 2003 00:28:23 -0600
Message-ID: <CfWcnVmHYOQa9kiiXTWc-w@speakeasy.net>


Here is another approach (only first half of the page applies here) I was emailed personally in response to my orginal post:

http://fungus.teststation.com/~jon/treehandling/TreeHandling.htm

Basically, the (too obivious for me to think of ;-) concept appears to be storing a mapping of the Node / Parent for every parent in the chain. Basically it splits up the materialized view concept into multiple rows, or one can think of it as the adjancency list with all parents stored. Perhaps call this the "Materialized List".

Personally, this is my likely favorite since I tend to "trust" the performance of giant tables that are nothing more than 2 columns of integers. Seems like this approach would handle most of the desired tree cases (select path & child count, insert, delete, move) very well.

Hopefully postgres can handle a very active, very narrow 50 million row table without breaking a sweat.

"Arjen van der Meijden" <acmmailing_at_vulcanus.its.tudelft.nl> wrote:

>> Rick Gigger wrote:
>> 
>> I was glad to see this topic come up on the list as I was 
>> about to start asking about some of these issues myself.  I 
>> would like to discuss each of the methods I have researched 
>> so far for doing trees in sql and see if anyone has some 
>> experience or insite into the topic that could help me.

>
> Have a look here: http://www.scenic-route.com/program/db/lists.htm
> It is quite a nice overview with some advantages and disadvantages of
> each method.
>
>> I have a lot of thouhts on this but here is my first question:
>>
>> In the first article at the end of the section on materialized paths
>> and the beginning of the nested set section Tropashko basically says
>> that neither one really does a good job at answering "who are all of
>> my ancestors" but that the materialized path method has a nice kludge
>> that you can do with some funky string manipulation.

>
> I don't see how the nested intervals-query is better/faster than the
> nested set approach, but both seem to be possibly using indices.
> The nested set uses a simple "where left between parent.left and
> parent.right", if you happen to have those numbers in your application's
> memory, you could even build your query directly like that and save
> yourself a self join.
> Another approach, I used, is something like:
> Select * from nset n1, (select (distinct) * from nset where nset.id =
> $parentid) as n2 where n1.left between n2.left and n2.right
> (the distinct will force a materialization, which might improve the
> performance or not, in my tests it did)
>
> With the materialized path you'll have to use a like-search (child.path
> like parent.path || '%'), where hopefully the optimiser notices that it
> can chop off the end of the string and just look at the first part
>
>> Is this true?  Celko in his articles seems to make it sound
>> like this query will be very fast.  But Tropashko it seems

> It'll use an index range-search, so I don't see how it can be faster,
> except for a hash/index lookup or so (which is possible with the
> transitive closure version of an adjacency list).
>
>> is saying that it will be slow. Am I reading this right?  If
>> so is Tropashko right?  Any ideas on this?  Any articles / papers
>> that might shed some light on this specific question or the
>> topic in general?

> The above article is a nice one to read I think.
>
> I'll try to summarize my thoughts on them, since I'm looking into an
> efficient tree approach myself aswell:
> All methods have both advantages and disadvantages and it'll depend on
> your situation whether that is a showstopper or not. All are bad when
> you want to remove a node from the tree, but the insert/update penalties
> depend on the situation.
>
> * The adjancency list is lightning fast with inserts, updates but a bit
> clumsy with deletions (you need to connect the direct children to
> another element, that's all). It'll be very fast with the two simple
> queries "who are my direct children" and "who is my parent", but you
> need either a recursive approach or some enhancement like a transitive
> closure-graph to enhance queries like "who are my predecessors" and "who
> are all my ancestors".
>
> So if you'll have a large tree, only few a levels deep and a lot of
> inserts and/or subtree movements, this seems to be the best approach.
> And you can store "max int"-number of nodes.
>
> * The materialized path is not so very efficient in terms of storage, it
> does inserts fast, but updates and deletions are slow. Retrieval of all
> ancestors is fast, retrieval of the predecessors is extremely trivial,
> but retrieval of the direct parent and/or children is somewhat more
> difficult (you'll need to look at the depth, if you do that often a
> functional-index might be handy).
> Perhaps the ltree-implementation in contrib/ltree is worth a look and
> encoding the trees in much more dense encodings (like a 256bit encoding
> I saw mentioned earlier and skipping the dot for just a single-bit
> terminator) makes it less inefficient.
>
> So if you do a lot of inserts, not so many updates and deletes and have
> much need for the entire list of predecessors/ancestors, I suppose this
> one is quite nice. But it is not so efficient in terms of storage, so
> very large/deep trees impose a huge overhead since each node stores its
> entire path.
>
> * The nested set is inefficient with insertions, updates and deletions
> but much more efficient with storage than the MP. To speed up the
> process of selecting only the direct parent/children you can use a depth
> field (redundant, but handy) which'll save you one or two extra
> selfjoins.
> For relatively static trees the nested set is good, but actively
> changing trees are very bad for your performance. You can store "max
> int"/2 nodes in this approach.
>
> * The nested intervals use the same approach as the nested set, but uses
> a static encoding. This allows you to do very efficient inserts, so the
> author claims. I have my doubts dough, if you don't know the number of
> children of your parent and just want to do "connect this child to that
> parent", it'll be more difficult, you'll need to find that parent, count
> it's children, decide the encoding-number of this new child and then you
> can calculate its new numbers.
> Still more efficient than the nested set, but not so efficient and you
> DO need to look into your database, while the author claimed you didn't
> need to.
> I havent't worked with this approach yet, but I saw the author use a lot
> of functions in his queries, I'm not sure whether that is a good idea,
> it might affect the usability of your indices...
> Another disadvantage is its very inefficient use of the integer-values
> available, it can only have a depth of 32 with normal integers, afaik
> and not so many children on a level as you'd like perhaps. The author
> suggests defining a unlimited integer, which is not so good for your
> performance at all (search for '"nested interval" sql' in google or so
> and you'll find his messages on the dbforums).
>
> * His other approach, the single-integer version, is even worse in terms
> of efficient integer-use, you can have only 32 levels at the best case
> (the left most branch only!) and only about 30 nodes next to each other
> in the same bestcase (since the numbers increase exponantional: level1 =
> 5, 11, 23, 47, 95, etc). The worst case (the right most branch) can
> possibly store only one or two levels with only one or two nodes...
>
> So the claimed advantage of the better performance is a bit limited,
> you'll either need *very* large integers to store large trees, or you
> are simply limited in the size of your tree by some relatively small
> numbers. And that is a bit sad, since bad performance is only a
> problem/visible with large(r) trees.
>
> I'm not sure whether the above summary is correct, anyone any idea? I've
> to use it in a research paper for my study anyway, so expanding my
> thoughts in an email is a nice test :)
> Please comment.
>
> Best regards,
>
> Arjen van der Meijden
>
>
>
>
> ---------------------------(end of broadcast)---------------------------
> TIP 9: the planner will ignore your desire to choose an index scan if your
> joining column's datatypes do not match
>
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Received on Tue Dec 09 2003 - 00:28:23 CST

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